Document Type
Article
Publication Date
2-1-2012
Published In
Proceedings Of The Royal Society Of Edinburgh, Section A: Mathematics
Abstract
We are concerned with the solvability of nonlinear second-order elliptic partial differential equations with nonlinear boundary conditions. We study the generalized Steklov-Robin eigenproblem (with possibly singular weights) in which the spectral parameter is both in the differential equation and on the boundary. We prove the existence of solutions for nonlinear problems when both nonlinearities in the differential equation and on the boundary interact, in some sense, with the generalized spectrum. The proofs are based on variational methods and a priori estimates.
Recommended Citation
Nsoki Mavinga.
(2012).
"Generalized Eigenproblem And Nonlinear Elliptic Equations With Nonlinear Boundary Conditions".
Proceedings Of The Royal Society Of Edinburgh, Section A: Mathematics.
Volume 142,
Issue 1.
137-153.
DOI: 10.1017/S0308210510000065
https://works.swarthmore.edu/fac-math-stat/78
Comments
This work is freely available courtesy of Cambridge University Press and The Royal Society of Edinburgh.
©2012 The Royal Society of Edinburgh
First published online January 30, 2012: https://doi.org/10.1017/S0308210510000065.